Find the value of the ${96^{{\text{th}}}}$ term of the sequence.

The first term of a geometric sequence is $6$. The ${6^{{\text{th}}}}$ term of the geometric sequence is equal to the ${17^{{\text{th}}}}$ term of the arithmetic sequence given above.

Write down an equation using this information.

The first term of a geometric sequence is $6$. The \${6^{{\text{th}}}}$ term of the geometric sequence is equal to the ${17^{{\text{th}}}}$ term of the arithmetic sequence given above.

Calculate the common ratio of the geometric sequence.

${u_{96}} = {u_1} + 95d$     (M1)

$= 0 + 95 \times 12$

$= 1140$     (A1)     (C2)

[2 marks]

$6{r^5} = 16d$     (A1)

$6{r^5} = 16 \times 12$ ($192$)     (A1)     (C2)

Note: (A1) only, if both terms seen without an equation.

[2 marks]

${r^5} = 32$     (A1)(ft)

Note: (ft) from their (b).

$r = 2$     (A1)(ft)     (C2)

[2 marks]

Part (a) was done well. There was some confusion in answering part (b) with many candidates unsure what they needed to write down. Often the two terms were seen somewhere in the working without the equation being written down in the answer box, or the equation was seen in the working for part (c). Part (c) was answered well, often with follow-through marks being awarded from an incorrect part (b) provided the working was seen.

Part (a) was done well. There was some confusion in answering part (b) with many candidates unsure what they needed to write down. Often the two terms were seen somewhere in the working without the equation being written down in the answer box, or the equation was seen in the working for part (c). Part (c) was answered well, often with follow-through marks being awarded from an incorrect part (b) provided the working was seen.

Part (a) was done well. There was some confusion in answering part (b) with many candidates unsure what they needed to write down. Often the two terms were seen somewhere in the working without the equation being written down in the answer box, or the equation was seen in the working for part (c). Part (c) was answered well, often with follow-through marks being awarded from an incorrect part (b) provided the working was seen.